I love both so much! I love Delphine personaly, but. Hm. I love Delphine because I absolutely adore Delphi, unfortunately it automatically directs people's thoughts to the Oracle of Delphi, and sometimes I think Delphine might inadvertently do the same? I know, I'm an odd duckling, haha. Of the two, I would go with Daphne. It's got a fresh air to it, and no real name associations that I can think of.

“Never forget who you are, for surely the world won’t. Make it your strength. Then it can never be your weakness. Armor yourself in it, and it will never be used to hurt you.”
― George R.R. Martin, A Game of Thrones